Generalized Survival Signature for Repairable Systems: Optimal Allocation of Minimal Repairs
针对可修系统的最小维修模型，提出广义生存签名（rGSS）并推导系统可靠性的混合表示，进而开发出在任意相干系统中基于最小割（路）集的两组件间以及四种常见系统结构（串联、并联、串并联、并串联）中所有组件间的最优维修分配策略。
ABSTRACT The minimal repair model is a fundamental framework for analyzing repairable systems. Optimizing the allocation of limited repair resources under this model is both important and challenging. This study introduces an efficient approach based on system signatures to address this problem. We first propose the generalized survival signature for repairable systems (rGSS) and derive a key mixture representation of system reliability. This extends the traditional signature concept beyond repairable series systems to general coherent systems. Leveraging the rGSS, we develop optimal repair allocation strategies between two specific components with comparative criticality via minimal cut (path) sets in arbitrary coherent systems, as well as among all components in four common system structures: Series, parallel, parallel‐series, and series‐parallel. Numerical examples are provided to illustrate the optimality of the proposed strategies and explore their potential for generalization.